# Series Resonance with Variable Frequency

Series resonance is a resonance condition that usually occurs in series circuits, where the current becomes a maximum for a particular voltage level. A series circuit containing R, L and C is said to be in resonance when the total reactance is zero. Since the capacitive reactance and the inductive reactance are of opposite sign so a series circuit will be in resonance when XL is equal to XC in magnitude. Thus from the equation bellow, we can measure series resonance.

Where f is the resonance frequency. Thus series resonance can be obtained by adjusting L, C or f. In this experiment we will vary frequency (f) to obtain the resonance condition. It is obvious that at the resonance the power factor of the combined load will be unity, and the total impedance will be minimum so that current is minimum. This is the criterion, with which we will detect the resonance condition.

### Required Equipment

• Oscilloscope
• Signal generator
• Resistor
• Inductor
• Capacitance
• Voltmeter

### Circuit Diagram

Here the circuit connection for Observing Series Resonance is given bellow using our given equipment.

### Procedure

1. Put the connection according the given circuit diagram.
2. At first we will have to complete the RLC circuit by setting 100 Ohm resistance, 10 mH inductance and 50 nF capacitance. Also connect the 100 W resistance (R1) to measure the current.
3. Connect the voltage across the RLC load as input to the channel 1 of the oscilloscope, and the voltage across the 100 Ohm resistance as channel 2.
4. Observe the wave-shape in both channels separately and in dual mode. Measure the values of the current IS, voltage V load and the phase difference between V load and IS. It is point to be noted, which wave leads.
5. Also have to measure the voltage across the resistor, inductor and capacitor by voltmeter.
6. Increase the frequency gradually until series resonance is obtained.
7. Repeat the measurements of step 4 and 5 for different frequency. At each step, adjust the signal generator output so that VS remains constant
8. Continue to increase the frequency until the current lags the voltage by about 45 degree . We will have to repeat all measurements in each step.
9. The series resonant current curve increases to a maximum at resonance then decreases when the resonance is passed.

JeionAhmed